They have been hailed as a miracle solution to sleepless nights, and parents are clamouring to get their hands on them.
The internet is buzzing with tales of the Lulla Doll, a soft toy designed to soothe children to sleep, and the "magical" dolls are now virtually impossible to find because of the high demand.
The doll was created by an Icelandic psychologist, who wanted to find a children's sleep aid that would imitate closeness to a parent or caregiver. The dolls have a soft outer covering, and make heartbeat and breathing noises, which are comforting to babies.
Some parents say the dolls sound similar to Darth Vader, and are so loud they can be heard in an adjacent room, but many agree that they work - and there's also the science to prove it.
The team who created the doll tested it in the newborn intensive care unit of Iceland National Hospital, and found they had a range of benefits for premature tots.
The researchers said the doll helped babies to fall asleep sooner, promoted less stress and crying, and helped the babies' heartbeat and breathing to stabilise.
The initial release of just 5000 Lulla Dolls quickly sold out, and there are waiting lists around the world for the eagerly awaited second shipment.
The dolls, which retail for about $100, have been attracting fierce bidding wars and reaching up to $350 on online auction site, eBay.
Other parents have been putting out desperate calls to Facebook in an effort to track down the dolls.
The toy distributor, Roro Care, is said to be working with suppliers throughout the UK, Australia and New Zealand to fill demand.